Learning paths
- Lessons
- 94
- Topics
- 93
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Pure, first pass
27 lessons
- 2 lessonsFreeAlgebra entry check: indices, surds and exact valuesPure 1 · Ch 1.1
- Quadratics: square form, discriminants and rootsPure 1 · Ch 2.1
- Linear and quadratic simultaneous equationsPure 1 · Ch 3.1
- Inequalities and solution setsPure 1 · Ch 3.4
- Polynomial algebra and the factor theoremPure 1 · Ch 1.2
- Sketching polynomial and reciprocal graphsPure 1 · Ch 4.1
- Lines, gradients and perpendicularityPure 1 · Ch 5.1
- Circles, tangents and intersectionsPure 1 · Ch 6.1
- Shifts, stretches and reflectionsPure 1 · Ch 4.5
- Deduction, exhaustion and counterexamplesPure 1 · Ch 7.4
- Vectors: components, position and subtractionPure 1 · Ch 11.1
- Magnitude, direction and vector geometryPure 1 · Ch 11.3
- Unit-circle trigonometry and periodic graphsPure 1 · Ch 9.5
- Trig identities and interval equationsPure 1 · Ch 10.3
- Non-right triangles and the ambiguous casePure 1 · Ch 9.1
- Radians, arc lengths and sector areasPure 2 · Ch 5.1
- Exponential graphs and transformationsPure 1 · Ch 14.1
- Logarithms and exponential equationsPure 1 · Ch 14.4
- Exponential models and their parametersPure 1 · Ch 14.3
- Derivatives from first principlesPure 1 · Ch 12.1
- Power, exponential and basic trig derivativesPure 1 · Ch 12.3
- Tangents, normals and increasing/decreasing intervalsPure 1 · Ch 12.6
- Stationary points, optimisation and curvaturePure 1 · Ch 12.8
- Antiderivatives and the fundamental theoremPure 1 · Ch 13.1
- Definite integrals, areas and limiting stripsPure 1 · Ch 13.4
- Integer binomial expansions and coefficientsPure 1 · Ch 8.1
Statistics, first pass
13 lessons
- Sampling and the population questionStats & Mech 1 · Ch 1.1
- Meet the LDS: locations, units and cleaningStats & Mech 1 · Ch 1.5
- Histograms, box plots and cumulative frequencyStats & Mech 1 · Ch 3.1
- Averages, spread and grouped percentilesStats & Mech 1 · Ch 2.1
- Variance, standard deviation and codingStats & Mech 1 · Ch 2.4
- Scatter plots, regression and contextual interpretationStats & Mech 1 · Ch 4.1
- Sample spaces, exclusivity and independenceStats & Mech 1 · Ch 5.1
- Conditional probability: trees, tables and setsStats & Mech 2 · Ch 2.1
- Probability assumptions and model criticismStats & Mech 1 · Ch 5.3
- Discrete random variables and binomial assumptionsStats & Mech 1 · Ch 6.1
- Binomial point and cumulative probabilitiesStats & Mech 1 · Ch 6.2
- Hypothesis tests for a binomial proportionStats & Mech 1 · Ch 7.1
- Year-one model and calculator clinicPure 1 · Ch 14.3
Mechanics, first pass
9 lessons
- Mechanics units and signed quantitiesStats & Mech 1 · Ch 8.3
- Position, displacement, distance, speed and velocityStats & Mech 1 · Ch 8.3
- Motion graphs and area/gradient reasoningStats & Mech 1 · Ch 9.1
- Constant-acceleration equations and derivationsStats & Mech 1 · Ch 9.3
- Force diagrams, weight and Newton's first lawStats & Mech 1 · Ch 10.1
- Newton's second law in one dimensionStats & Mech 1 · Ch 10.3
- Equilibrium and Newton's third-law pairsStats & Mech 1 · Ch 10.1
- Connected particles and smooth pulleysStats & Mech 1 · Ch 10.5
- Variable-acceleration motion in one dimensionStats & Mech 1 · Ch 11.1
Pure, second pass
30 lessons
- Composite/inverse functions and domain/rangePure 2 · Ch 2.2
- Modulus graphs, equations and inequalitiesPure 2 · Ch 2.1
- Rational expressions and partial fractionsPure 2 · Ch 1.2
- Recursive sequences, monotonicity, periodicity and sigmaPure 2 · Ch 3.6
- Arithmetic progressions and proof of their sumPure 2 · Ch 3.1
- Geometric progressions and convergencePure 2 · Ch 3.3
- Sequences and series as financial/physical modelsPure 2 · Ch 3.8
- Rational binomial expansions and approximationPure 2 · Ch 4.1
- Reciprocal and inverse trig functionsPure 2 · Ch 6.1
- Addition, double-angle and half-angle identitiesPure 2 · Ch 7.1
- R-sine/cosine forms and extremaPure 2 · Ch 7.5
- Advanced trig equations and proofsPure 2 · Ch 7.4
- Small-angle approximationsPure 2 · Ch 5.5
- Periodic models and realistic domainsPure 2 · Ch 7.7
- Linearising power/exponential models with logsPure 1 · Ch 14.8
- Product, quotient and chain rulesPure 2 · Ch 9.1
- Implicit differentiation and parametric curvesPure 2 · Ch 8.1
- Parametric models, tangents and parameter domainsPure 2 · Ch 8.5
- Connected rates and setting up differential equationsPure 2 · Ch 9.10
- Standard advanced integrals and trig rewritesPure 2 · Ch 11.1
- Integration by substitutionPure 2 · Ch 11.5
- Integration by parts, including repeated usePure 2 · Ch 11.6
- Rational integration and logarithmic formsPure 2 · Ch 11.7
- Area between curves and parametric areasPure 2 · Ch 11.8
- Separable differential equations and interpretationPure 2 · Ch 11.10
- Bracketing roots and failure of sign-change argumentsPure 2 · Ch 10.1
- Fixed-point iteration and staircase/cobweb diagramsPure 2 · Ch 10.2
- Newton-Raphson, failure cases and contextual rootsPure 2 · Ch 10.3
- Trapezium estimates and boundsPure 2 · Ch 11.9
- Contradiction and first-principles proof clinicPure 1 · Ch 12.2
Statistics, second pass
6 lessons
- Normal distributions and calculator probabilitiesStats & Mech 2 · Ch 3.1
- Inverse Normal, standardisation and unknown parametersStats & Mech 2 · Ch 3.3
- Normal approximation to binomial and suitabilityStats & Mech 2 · Ch 3.6
- Tests for a Normal meanStats & Mech 2 · Ch 3.7
- Correlation tests and population parametersStats & Mech 2 · Ch 1.2
- LDS investigation: sampling to a defensible conclusionStats & Mech 1 · Ch 1.1
Mechanics, second pass
6 lessons
- Two-dimensional motion with vectors and calculusPure 2 · Ch 12.1
- Projectiles: components, trajectories and heightStats & Mech 2 · Ch 6.1
- Resolving forces, resultants and inclined planesStats & Mech 2 · Ch 5.1
- Friction: equilibrium, limiting cases and slidingStats & Mech 2 · Ch 5.3
- Moments and rigid-body equilibriumStats & Mech 2 · Ch 4.1
- Ladders, rods and connected-system modelsStats & Mech 2 · Ch 7.2
Paper workshops
3 lessons
Independent practice for Pearson Edexcel A-level Mathematics (9MA0), not endorsed by Pearson.